I could see racial feats (let's call them "racial awakening" so that it makes sense that you didn't have it at level 1) that give elves the fey type, dragonborn the dragon type, etc.
I suppose that would at least be a tolerable way of dealing with it. But without that...it's just offensive to any concept of setting integrity.
Also as a related beef, in the case of centaur, I don't like that a PC has dual type, but the monsters don't. Having multiple types is a part of your essence that affects how magic effects you. To say that just because you're an PC, you are subject to hold person and charm person and get the benefit of the beneficial humanoid spells (which I'm pretty sure exist, but aren't immediately coming to mind) is way more annoying to me than saying that the centaur in the MM gets unlimited charges because it is an elite warrior, and PCs can learn that with a feat, like the svirfneblin and drow can pick up some of their advanced racial features as feats.
But then again, when I think about it, having size Large PCs follow the normal rules is problematic, because some of the hit points of a Large creature are pure meat, and they need more of them than a 1st-level PC can have.
Probably just best to not create PC races from Large monsters. Instead, we could have some rules for monsters as characters that assigned a monster level of some sort. 3e's ECL system might have sucked in implementation, but it was the right idea in concept.